*
Jacque Melin – GVSU
www.formativedifferentiated.com
Differentiation is a set of instructional strategies.
Reality: Differentiation is a philosophy—a way of
thinking (MINDSET) about teaching and learning. It
is, in fact, a set of principles.
*
Fixed Mind-Set
STUDENT
Growth Mind-Set
*Mindset – Carol Dweck
Teacher may underestimate
student capacity and
willingness to work hard and
“teach down” because
of the student’s language,
culture, economic status,
race, label, etc.
Both teacher and student study
student growth, set goals for
progress, and look for ways to
continue development.
Students at all readiness levels
have maximum opportunity for
challenge, growth, and success.
Both teacher and student
accept the student’s
difficulties as given, and
neither exerts the effort
needed for high levels of
student achievement. Both
also accept high grades on
grade-level work as adequate
for advanced learners.
Teacher encourages and insists
on student effort and growth.
Over time, the student’s mindset can change to a growth
orientation with evidence that
effort leads to success.
Students at all readiness levels
have maximum opportunity for
challenge, growth, and success.
Fixed Mind-Set
Growth Mind-Set
TEACHER
Differentiation
C. Tomlinson
Is a teacher’s response to learner’s needs
Guided by general principles of differentiation
Meaningful tasks
Quality Curriculum
Content
Flexible grouping
Continual assessment
Teachers can differentiate through
Process
Product
Building Community
Affect/Environment
According to students’
Readiness
Interest
Learning Profile
Through a variety of instructional strategies such as:
RAFTS…Graphic Organizers…Scaffolding …Cubing…Tic-Tac-Toe…Learning
Contracts….Tiering… Learning/Interest Centers… Independent Studies…Intelligence
Preferences….Orbitals…..Complex Instruction…ETC.
*It’s adequate for a district or school leader (or
professional developers) to tell, or even show,
teachers how to differentiate instruction
effectively.
*Reality: Learning to differentiate instruction well requires
rethinking one’s classroom practice and results from an
ONGOING process of trial, reflection, and adjustment in the
classroom itself.
*
*
*Differentiation is something a teacher does or doesn’t do (as
in, “I already do that,” or “I tell our teachers that they
already differentiate instruction.”).
*Reality: Most teachers who remain in a classroom for longer
than a day do pay attention to student variation and respond
to it in some way.
*However, very few teachers proactively plan instruction to
consistently address student differences in readiness, interest,
and learning profile.
*
How to Differentiate
Name:
Date:
Fogarty & Pete,
2011
Change the Content
Change the Content
 Complexity
 Resources
 Environment
Change the Content
 Complexity
Concrete to Abstract
 Resources
Text/Media
 Environment
TAPS
Do/View/Construe
DO – Manipulatives: Concrete
• Algebra Tiles (for linear and quadratic equation
solving)
• Didax Geofix (nets)
• Models of shapes (surface area and volume)
• Soft 1 cm squares
http://www.etacuisenaire.com
• Virtual Manipulatives
http://www.neirtec.org/activities/math_portal.htm
• Wolfram Alpha
http://www.wolframalpha.com/
VIEW – Graphic
Organizers Representational
www.graphicorganizers.com
Name ________________
Graph the related function.
Identify the x-intercepts.
Class ________________
y
Equation _______________
x
Solve the equation by
completing the square.
Solve the equation by
factoring.
State the discriminant of the
equation and the number of
solutions.
Solve the equation using the
quadratic formula.
Each student will be given a problem to solve in a variety ways based on his or her performance
on a pre-assessment instrument. The level one problem is the easiest among the group while the
level five problem is the most challenging.
(1) Level One: x 2  2 x  8  0
Which method is most direct
in finding the solution to the
equation? Why?
(2) Level Two: 9 x 2  30 x  25  0
(3) Level Three: x 2  6 x  1
(4) Level Four: 2 x 2  3x  2  0
(5) Level Five: 5 x 2  8 x  1
http://challengebychoice.wordpress.com/examples-of-tiered-math-assessments/
*3 Levels of Challenge - CbC
Green—Tasks are foundational and appropriate for the current
grade level. Success depends on understanding and applying
required knowledge and skills. Green level tasks meet a
rigorous grade level proficiency standard.
Blue—Tasks are advanced and complex. Success depends on
extending one’s skills in order to recognize and address the
added layers of complexity.
Black—Tasks are extremely advanced and highly complex.
Success depends on creatively applying and extending one’s
skills, at times in very unfamiliar territory.
Change the Process
Change the Process
 Direct Instruction
 Cooperative Learning
 Inquiry
Change the Process
 Direct Instruction
Hook them
Curiosity
Novelty
 Cooperative Learning
Each one – Teach one
 Inquiry
PBL
*
*
1.
2.
3.
4.
5.
6.
Awareness
Comprehension
Application
Analysis
Synthesis
Evaluation
S. Gendron, Kentwood presentation, March 2011
*
1. Knowledge in one discipline
2. Application within discipline
3. Application across disciplines
4. Application to real-world predictable situations
5. Application to real-world unpredictable
situations
S. Gendron, Kentwood presentation, March 2011
Levels
Bloom’s
6
5
4
3
2
1
C
D
A
B
1
2 3 4 5
Application
S. Gendron, Kentwood presentation, March 2011
Rigor/Relevance Framework
6
•
•
5
4
•
Analyze the graphs of the
perimeters and areas of squares
having different-length sides.
Determine the largest
rectangular area for a fixed
perimeter.
Determine and justify the
similarity or congruence for two
geometric shapes.
C
1
•
•
•
3
2
•
• Express probabilities as fractions,
percents, or decimals.
• Classify triangles according to
angle size and/or length of sides.
• Calculate volume of simple
three- dimensional shapes.
• Given the coordinates of a
quadrilateral, plot the
quadrilateral on a grid.
A
1
2
Obtain historical data about local
weather to predict the chance of
snow, rain, or sun during year.
Test consumer products and illustrate
the data graphically.
Plan a large school event and
calculate resources (food,
decorations, etc.) you need to
organize and hold this event.
Make a scale drawing of the
classroom on grid paper, each group
using a different scale.
D
• Calculate percentages of advertising in
a newspaper.
• Tour the school building and identify
examples of parallel and perpendicular
lines, planes, and angles.
• Determine the median and mode of
real data displayed in a histogram
• Organize and display collected data,
using appropriate tables, charts, or
graphs.
B
3
4
5
S. Gendron, Kentwood presentation, March 2011
*
Questgarden
The Buck Institute
Change the Product
Change the Product
 Entry Points
 Expressive Modes
 Accountability
Change the Product
 Entry Points
How they learn
 Expressive Modes
How they express it
 Accountability
How we grade/score it
Formative/Portfolios/Performance Based
Change the Product
 Entry Points
How they learn
 Expressive Modes
How they express it
 Accountability
How we grade/score it
Formative/Portfolios/Performance Based
Story Elements: Tic-Tac-Toe Board
(Auditory, Visual, Kinesthetic)
Target:
I can describe the elements
of a story (characters,
setting, plot).
*
one activity from
each horizontal row
Create a pair of collages that compares
you and a character in the book.
Compare and contrast physical and
personality traits. Label your collages so
viewers understand your thinking.
Write a bio-poem about yourself
and another about a main
character in the book so your
readers see how you and the
character are alike and different.
Be sure to include the most
important traits in each poem.
Write a recipe or set of directions
for how you would solve a problem
and another for how a main
character in the book would solve
a problem. Your list should help
us know you and the character.
Draw/paint and write a greeting card that
invites us into the scenery and mood of
an important part of the book. Be sure
the verse helps us understand what is
important in the scene and why.
Make a model or a map of a key
place in your life, and an important
one in the novel. Find a way to
help viewers understand both what
the places are like and why they
are important in your life and the
characters’.
Make 2 timelines. The first should
illustrate and describe a least 6-8
shifts in settings in the book. The
second should explain and
illustrate how the mood changes
with the change in setting.
Using books of proverbs and/on
quotations, find at least 6-8 that you feel
reflect what’s important about the novel’s
theme. Find at least 6-8 that do the
same for your life. Display them and
explain your choices.
Interview a key character from the
book to find out what lessons
he/she thinks we should learn from
events in the book. Use a Parade
magazine for material. Be sure
the interview is thorough.
Find several songs you think
reflect an important message from
the book. Prepare a Podcast.
Write an exhibit card that helps
your listener understand how you
think these songs express the
book’s meaning.
Novel Title: ____________________ Author:_______________________
Activities Selected: _______, _____, _____
Student: ______________________
Counting Principles & Probability: Tic-Tac-Toe
Board
(Auditory, Visual, Kinesthetic)
Targets:
•I can write the steps of a math induction proof for a
given series.
•I can apply Pascal’s Triangle to find the coefficients of
a binomial expansion.
•I can apply the Binomial Theorem to expand a
binomial.
•I can find probabilities of mutually exclusive &
independent events.
V. Thomasma, Kentwood
Counting Principles & Probability
Tic-Tac-Toe Board
Choose three activities in a row (horizontally, vertically, or diagonally) to complete. The activities are
designed to help you relate to and remember probability concepts. They are due at the end of the unit, so
please work on them after completing daily work in class, or at home. You may work by yourself or with one
other person on any or all three activities.
1. Letter of Advice
Write a letter to a friend who is in
Algebra 2 this year, and going to
take Precalculus next year. Don’t
scare them! Instead, list and
describe four pieces of advice that
would help them succeed in
Precalculus. Stretch your brain, and
make at least 2 pieces of advice
relevant to this unit.
2. In The News
Pretend you are a journal reporter in
the 1600s. (You’ll also need to
pretend they had TV and reporters
then!) Your job is to describe the
controversy over Pascal’s
Triangle…did Blaise Pascal really
discover it? Should it be named
after him? Use the internet to
conduct some research. Plan it out
ahead of time, then create a short
clip (less than 5 minutes) with a
video camera.
3. Graphing Calculator Activity
Create 5 probability problems that
are solved most efficiently with a
Graphing Calculator. (Hint: using
combinations, permutations and
The Binomial Theorem guarantees
this). Make at least 2 of the
problems real-life scenarios.
Include the answers as well.
(Interpersonal/Linguistic)
(Bodily/Kinesthetic)
(Mathematical/Logical)
4. Poem or Rap
Write a poem or rap about either
permutations & combinations,
Pascal’s Triangle, or The Binomial
Theorem. Be sure to include
information that will give your
fellow math students a clever way of
remembering how to use the
mathematical skill you chose! Your
work may be either read or performed
for the class.
5. Jeopardy Review Game
Write Jeopardy questions that can be
used to review our Probability Unit.
Include 10 questions with answers.
Use an index card for each question,
with the answer on the back. We
will use 6 categories, which are the
titles of the lessons in your book.
Write at least one question for each
category.
6. Poster
It is your chance to make a cheat sheet
for your classroom! Design and
make a poster that includes the
important concepts from this unit.
Make it colorful, and include at least
2 relevant pictures or drawings. It
will be displayed in the classroom,
until test day of course!
(Musical/Rhythmic)
(Linguistic/Intrapersonal)
(Visual/Spatial)
7. Internet Research
Search the Internet to find 5 games
that use Combinatorics
(permutations or combinations).
Begin at Mrs. Thomasma’s Math of
Games website:
www.mathematicsofgames.pbwiki.co
m
For each game, write a brief
description of the game, which
combinatorics are used, and how
knowledge of the math might help
with strategy!
(Intrapersonal)
8. Comic Strip
Create a comic strip that highlights a
concept about probability, counting
principles, math induction, or
another topic from our unit.
Include illustrations and dialogue.
9. Nature Walk
Take a walk outside to brainstorm
examples of arithmetic and
geometric patterns that occur in
nature. You may consider
architecture also. Record at least
four of your observations. Draw or
take pictures of them, and explain
which type of sequence each
exemplifies.
(Visual/Spatial)
(Naturalist)
Story Response: Choice Board
(Triarchic Intelligences)
TARGET:
I can describe the theme or
message that a writer or
author wants to
communicate.
Analytic
Listen to or read a story and create a chart
that tells events in the story and how they
contribute to the theme of the story.
Practical
Think of a time you or someone you know
was in a situation similar to the main
character in the story. Draw and/or write
about it and include the theme or
message that was similar to the story.
Creative
Imagine that the story continues after the
last page. Use Prezi or PowerPoint or act
out the next scene. This scene should
relate to the theme or message of the
story.
Cells: Choice Board
(Triarchic Intelligences)
TARGETS:
Know – I can name the parts of the cell & their
function
Understand - I can explain that a cell is a system
of interrelated parts
Do - I can analyze the interrelationships of cell
parts/functions and present understandings in a
clear, useful and interesting way
Analytic
Use a cause/effect chain or some other format you develop to
show how each part of a cell affects other parts as well as the
whole. Use labels, directional markers, and other symbols as
appropriate to ensure that someone who is pretty clueless
about how a cell works will be enlightened after they study
your work.
Practical
•
•
•
Creative
Look around you (in your world or the broader world) for systems
that could serve as analogies for the cell. Select your best analogy
(“best” = most clearly matched, most explanatory or enlightening).
Devise a way to make the analogy clear and visible to an audience
of your peers, ensuring that they will develop clearer and richer
insights about how a cell works by sharing in your work.
Be sure to emphasize both the individual functions of cell parts and
the interrelationships among the parts.
Use unlikely stuff to depict the structure and function of the cell, with
emphasis on interrelationships among each of the parts. You should
select your materials carefully to reveal something important about the
cell, its parts, and their interrelationships. Your “ahas” should trigger
ours.
OR
Tell a story that helps us understand a cell system with interdependent
actors or characters, a plot to carry out, a setting , and even a
potential conflict. Use your own imagination and narrative preferences
to help us gain insights into this remarkable system.
Immigration: Choice Board
(Triarchic Intelligences)
TARGET:
I can explain the meaning of
“melting pot,” “mosaic,” and
“salad bowl” as they relate to
immigration in America.
Analytic
Analyze how and why the U.S. population
has shifted from a melting pot to a salad
bowl or mosaic as it has assimilated new
immigrants. Show your analysis in a
diagram.
Practical
Think of the population of Grand Rapids and
Kent County. Is it better for Grand Rapids to
assimilate new people to this area like a
melting pot or a salad bowl? Defend your
position in a Podcast.
Creative
Create a different pair of metaphors to
characterize how immigrants assimilated in
the past and how they assimilate today.
Write an explanation for each or create a
visual to depict them.
Show-And-Tell Boards
All students have the same TASK,
but have a choice of SHOW AND
TELL.
Top row – what they could show
Bottom row – what they could tell
Need 1 SHOW & 1 TELL
* TARGET:
I can write in a technical format.
TASK: Write a set of directions for a
household task or school activity.
SHOW
Illustrations Diagram
How-to
or Flow
Brochure
Chart
TELL
Use topic
headings
and
paragraphs
Use
Write
detailed
detailed
numbered sentences
or bulleted
steps
* TARGET: I can describe events that occurred
during the civil rights movement
TASK: Describe a significant event that
occurred during the civil rights movement.
SHOW
Charts and
graphs
Timeline of
incidents
related to the
event
Illustrations,
photographs,
graphics, or
artifacts
TELL
Newspaper
article
Video news Speech
interview
Food Webs: Choice Board
(Show and Tell Board)
TARGETS:
• I can classify the role of
each organism in the food
web of an owl.
• I can explain the energy
flow in the food web of an
owl.
Task: Construct a food web with the owl at the highest trophic level. Be sure to
include producers (green plants) and decomposers in your food web. Also include
the Sun. The intermediate organisms should include the prey found in the owl
pellets that you dissected in class. Label the role of all organisms and use arrows
to show the energy flow between each organism. Finally, explain the flow of
energy in the food web.
*Make
Believe
Comix
*Glogster
*Go
Animate
QR
Codes
*Animoto
Do we differentiate by:
Whole group?
Small group?
Individual?
Do we differentiate by:
Whole group?
Multimodal – tap into
many ways of learning
Small group?
Instructional
Interventions
Individual?
Tutorials
Hook
Input
Interaction
Product
Assessment
Reflection
Hook – Role Play
Input –
(content)
Direct Instruction (Little Book) - Novelty
(content/process)
Interaction – 3 Musketeers
(process)
Product – Little Book on DI Theory
(product)
Assessment – Tell and Retell
Reflection – Scale of 1-10
As a team of educators:
Discuss with your peers the
differentiated instructional ideas
and strategies that you
recommend for implementation in
your unit.
Tic Tac Toe Choice Board,
Triarchic Choice Board,
Menu (Appetizer, Entrée, Dessert),
Show & Tell,
Think Dots
Tiered Assignment
*An Old African Proverb Asks
How do you eat
an elephant?????